%   ORIGINAL: 'h4/thm/quotient_pair/PAIR_MAP_RSP_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!R3 abs3 rep3. 'h4/const/quotient/QUOTIENT' R3 abs3 rep3 ==> (!R4 abs4 rep4. 'h4/const/quotient/QUOTIENT' R4 abs4 rep4 ==> (!f1 f2 g1 g2. 'h4/const/quotient/===>' R1 R2 f1 f2 /\ 'h4/const/quotient/===>' R3 R4 g1 g2 ==> 'h4/const/quotient/===>' ('h4/const/quotient_pair/#hash##hash##hash#' R1 R3) ('h4/const/quotient_pair/#hash##hash##hash#' R2 R4) ('h4/const/pair/#hash##hash#' f1 g1) ('h4/const/pair/#hash##hash#' f2 g2)))))
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!R3 abs3 rep3. 'h4/const/quotient/QUOTIENT' R3 abs3 rep3 ==> (!R4 abs4 rep4. 'h4/const/quotient/QUOTIENT' R4 abs4 rep4 ==> (!f1 f2 g1 g2. 'h4/const/quotient/===>' R1 R2 f1 f2 /\ 'h4/const/quotient/===>' R3 R4 g1 g2 ==> 'h4/const/quotient/===>' ('h4/const/quotient_pair/#hash##hash##hash#' R1 R3) ('h4/const/quotient_pair/#hash##hash##hash#' R2 R4) ('h4/const/pair/#hash##hash#' f1 g1) ('h4/const/pair/#hash##hash#' f2 g2)))))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f48736,V_3f48732]: ![F0, G0]: (![X]: s(V_3f48732,happ(s(fun(V_3f48736,V_3f48732),F0),s(V_3f48736,X))) = s(V_3f48732,happ(s(fun(V_3f48736,V_3f48732),G0),s(V_3f48736,X))) => s(fun(V_3f48736,V_3f48732),F0) = s(fun(V_3f48736,V_3f48732),G0))).
fof('h4/thm/quotient_pair/PAIR_MAP_RSP_', conjecture, ![E,F,G,H,A,B,C,D]: ![R1, Abs1, Rep1]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R1),s(fun(A,E),Abs1),s(fun(E,A),Rep1)))) => ![R2, Abs2, Rep2]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(B,fun(B,bool)),R2),s(fun(B,F),Abs2),s(fun(F,B),Rep2)))) => ![R3, Abs3, Rep3]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(C,fun(C,bool)),R3),s(fun(C,G),Abs3),s(fun(G,C),Rep3)))) => ![R4, Abs4, Rep4]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(D,fun(D,bool)),R4),s(fun(D,H),Abs4),s(fun(H,D),Rep4)))) => ![F1, F2, G1, G2]: ((p(s(bool,'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),R1),s(fun(B,fun(B,bool)),R2),s(fun(A,B),F1),s(fun(A,B),F2)))) & p(s(bool,'h4/const/quotient/===>'(s(fun(C,fun(C,bool)),R3),s(fun(D,fun(D,bool)),R4),s(fun(C,D),G1),s(fun(C,D),G2))))) => p(s(bool,'h4/const/quotient/===>'(s(fun('h4/type/pair/prod'(A,C),fun('h4/type/pair/prod'(A,C),bool)),'h4/const/quotient_pair/#hash##hash##hash#'(s(fun(A,fun(A,bool)),R1),s(fun(C,fun(C,bool)),R3))),s(fun('h4/type/pair/prod'(B,D),fun('h4/type/pair/prod'(B,D),bool)),'h4/const/quotient_pair/#hash##hash##hash#'(s(fun(B,fun(B,bool)),R2),s(fun(D,fun(D,bool)),R4))),s(fun('h4/type/pair/prod'(A,C),'h4/type/pair/prod'(B,D)),'h4/const/pair/#hash##hash#'(s(fun(A,B),F1),s(fun(C,D),G1))),s(fun('h4/type/pair/prod'(A,C),'h4/type/pair/prod'(B,D)),'h4/const/pair/#hash##hash#'(s(fun(A,B),F2),s(fun(C,D),G2)))))))))))).
